Hidden algebra of the N-body Calogero problem

A certain generalization of the algebra gl(N, ) of first-order differential operators acting on a space of inhomogeneous polynomials in ^N−1 is constructed. The generators of this (non-) Lie algebra depend on permutation operators. It is shown that the Hamiltonian of the N-body Calogero model can be represented as a second-order polynomial in the generators of this algebra. The representation given implies that the Calogero Hamiltonian possesses infinitely-many finite-dimensional invariant subspaces with explicit bases, which are closely related to the finite-dimensional representations of the above algebra. This representation is an alternative to the standard representation of the Bargmann-Fock type in terms of creation and annihilation operators.     

Radio-Frequency Hexamethyldisiloxane Plasma Deposition: A Comparison of Plasma- and Deposit-Chemistry

This study reports on the effect of input power to hexamethyldisiloxane (HMDSO) plasmas. The power dependence of the plasma-phase species and of the surface chemistry (of the deposits) has been investigated. Neutral and positive molecular species were detected within the plasma using mass spectrometry (MS). Secondary ion mass spectrometry (SIMS) was used to probe the molecular structure of the deposits. The elemental composition of the surface was determined by XPS and the deposition rate was monitored using a vibrating quartz crystal microbalance. Neutral and cationic molecules of mass greater than HMDSO were detected in the plasma. Their formation through ion-molecule reactions is proposed. Changes in the relative concentration of plasma-phase species follow those seen in molecular species detected at the deposit surface. Thus, we believe that the molecular structure of the deposits can be related to the species present in the plasma. While traditionally the dominant mechanism in deposit formation is assumed to be free radical combinations, we propose other possibilities involving cations with the aim of putting forward a new perspective on plasma polymerization mechanisms and thereby stimulating discussion.     

Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation

This paper is a direct continuation of [1] where we began the study of the integrable structures in Conformal Field Theory. We show here how to construct the operators ${\bf Q}_{\pm}(\lambda)$ which act in the highest weight Virasoro module and commute for different values of the parameter λ. These operators appear to be the CFT analogs of the Q - matrix of Baxter [2], in particular they satisfy Baxter's famous T- Q equation. We also show that under natural assumptions about analytic properties of the operators as the functions of λ the Baxter's relation allows one to derive the nonlinear integral equations of Destri-de Vega (DDV) [3] for the eigenvalues of the Q-operators. We then use the DDV equation to obtain the asymptotic expansions of the Q - operators at large λ; it is remarkable that unlike the expansions of the T operators of [1], the asymptotic series for Q(λ) contains the “dual” nonlocal Integrals of Motion along with the local ones. We also discuss an intriguing relation between the vacuum eigenvalues of the Q - operators and the stationary transport properties in the boundary sine-Gordon model. On this basis we propose a number of new exact results about finite voltage charge transport through the point contact in the quantum Hall system. Received: 2 December 1996 / Accepted: 11 March 1997     

Luminescent copolymers for applications in multicolor‐light‐emitting devices

Light‐emitting diodes based on organic materials [organic light‐emitting diodes (OLEDs)] have attracted much interest over the past decade. Several different attempts have been made to realize multicolor OLEDs. This article describes a new approach based on energy transfer in a donor/acceptor system. A copolymer containing both donor and acceptor compounds as comonomer units is prepared. The polymer consists of a derivative of a luminescent dye [4‐dicyanmethylene‐2‐methyl‐6‐4H‐pyran (DCM); acceptor compound], which is copolymerized with fluorene (donor compound) to combine the properties of an electroactive polymer with a highly luminescent dye. Photochemical processing is achieved by UV irradiation of this copolymer in the presence of gaseous trialkylsilanes. This reagent selectively saturates the C?C bonds in the DCM comonomer units while leaving the fluorene units essentially unaffected. As a result of the photochemical process, the red electroluminescence of the acceptor compound vanishes, and the blue‐green electroluminescence from the polyfluorene units is recovered. Compared with previous approaches based on polymer blends, this copolymer approach avoids problems associated with phase‐separation phenomena in the active layer of OLEDs. © 2006Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4317–4327, 2006     

Sobolev Spaces with only Trivial Isometries

We will give some conditions for Sobolev spaces on bounded Lipschitz domains to admit only trivial isometries.     

Rectification of sets in Euclidean spaces

We criticize traditional definitions of the arc length which require semi-continuity from below. Symmetric definitions of lower and uppern-lengths (n-dimensional volumes) are introduced for a wide class of sets in Euclidean spaces, and the additivity of both functionals is proved.     

The umbral calculus and orthogonal polynomials

We determine all orthogonal polynomials having Boas-Buck generating functions g(t)(xf(t)), where% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacqqHOo% qwcaGGOaGaamiDaiaacMcacqGH9aqpruqqYLwySbacfaGaa8hiamaa% BeaaleaacaaIWaaabeaakiaadAeacaqGGaWaaSbaaSqaaiaabgdaae% qaaOGaaeikaiaadggacaGGSaGaa8hiaiaadshacaqGPaGaaeilaiaa% bccacaqGGaGaaeiiaiaadggacqGHGjsUcaaIWaGaaiilaiaa-bcacq% GHsislcaaIXaGaaiilaiaa-bcacqGHsislcaaIYaGaaiilaiablAci% ljaacUdaaeaacqqHOoqwcaGGOaGaamiDaiaacMcacqGH9aqpcaWFGa% WaaSraaSqaaiaaicdaaeqaaOGaamOraiaabccadaWgaaWcbaGaaeOm% aaqabaGccaGGOaWaaSqaaSqaaiaaigdaaeaacaaIZaaaaOGaaiilai% aa-bcadaWcbaWcbaGaaGOmaaqaaiaaiodaaaGccaGGSaGaa8hiaiaa% dshacaGGPaGaa8hiamaaBeaaleaacaaIWaaabeaakiaadAeacaqGGa% WaaSbaaSqaaiaabkdaaeqaaOGaaeikamaaleaaleaacaaIYaaabaGa% aG4maaaakiaacYcacaWFGaWaaSqaaSqaaiaaisdaaeaacaaIZaaaaO% Gaaiilaiaa-bcacaWG0bGaaiykaiaacYcacaWFGaWaaSraaSqaaiaa% icdaaeqaaOGaamOraiaabccadaWgaaWcbaGaaeOmaaqabaGccaGGOa% WaaSqaaSqaaiaaisdaaeaacaaIZaaaaOGaaiilaiaa-bcadaWcbaWc% baGaaGynaaqaaiaaiodaaaGccaGGSaGaa8hiaiaadshacaGGPaGaai% 4oaaqaaiabfI6azjaacIcacaWG0bGaaiykaiabg2da9iaa-bcadaWg% baWcbaGaaGimaaqabaGccaWGgbGaaeiiamaaBaaaleaacaqGZaaabe% aakiaacIcadaWcbaWcbaGaaGymaaqaaiaaisdaaaGccaGGSaGaa8hi% amaaleaaleaacaaIYaaabaGaaGinaaaakiaacYcacaWFGaWaaSqaaS% qaaiaaiodaaeaacaaI0aaaaOGaaiilaiaa-bcacaWG0bGaaiykaiaa% -bcadaWgbaWcbaGaaGimaaqabaGccaWGgbGaaeiiamaaBaaaleaaca% qGZaaabeaakiaabIcadaWcbaWcbaGaaGOmaaqaaiaaisdaaaGccaGG% SaGaa8hiamaaleaaleaacaaIZaaabaGaaGinaaaakiaacYcacaWFGa% WaaSqaaSqaaiaaiwdaaeaacaaI0aaaaOGaaiilaiaa-bcacaWG0bGa% aiykaiaacYcaaeaadaWgbaWcbaGaaGimaaqabaGccaWGgbGaaeiiam% aaBaaaleaacaqGZaaabeaakiaacIcadaWcbaWcbaGaaG4maaqaaiaa% isdaaaGccaGGSaGaa8hiamaaleaaleaacaaI1aaabaGaaGinaaaaki% aacYcacaWFGaWaaSqaaSqaaiaaiAdaaeaacaaI0aaaaOGaaiilaiaa% -bcacaWG0bGaaiykaiaacYcacaGGUaGaa8hiamaaBeaaleaacaaIWa% aabeaakiaadAeacaqGGaWaaSbaaSqaaiaabodaaeqaaOGaaeikamaa% leaaleaacaaI1aaabaGaaGinaaaakiaacYcacaWFGaWaaSqaaSqaai% aaiAdaaeaacaaI0aaaaOGaaiilaiaa-bcadaWcbaWcbaGaaG4naaqa% aiaaisdaaaGccaGGSaGaa8hiaiaadshacaGGPaGaaiOlaaaaaa!C1F3!\[\begin{gathered}\Psi (t) = {}_0F{\text{ }}_{\text{1}} {\text{(}}a, t{\text{), }}a \ne 0, - 1, - 2, \ldots ; \hfill \\\Psi (t) = {}_0F{\text{ }}_{\text{2}} (\tfrac{1}{3}, \tfrac{2}{3}, t) {}_0F{\text{ }}_{\text{2}} {\text{(}}\tfrac{2}{3}, \tfrac{4}{3}, t), {}_0F{\text{ }}_{\text{2}} (\tfrac{4}{3}, \tfrac{5}{3}, t); \hfill \\\Psi (t) = {}_0F{\text{ }}_{\text{3}} (\tfrac{1}{4}, \tfrac{2}{4}, \tfrac{3}{4}, t) {}_0F{\text{ }}_{\text{3}} {\text{(}}\tfrac{2}{4}, \tfrac{3}{4}, \tfrac{5}{4}, t), \hfill \\{}_0F{\text{ }}_{\text{3}} (\tfrac{3}{4}, \tfrac{5}{4}, \tfrac{6}{4}, t),. {}_0F{\text{ }}_{\text{3}} {\text{(}}\tfrac{5}{4}, \tfrac{6}{4}, \tfrac{7}{4}, t). \hfill \\\end{gathered}\]We also determine all Sheffer polynomials which are orthogonal on the unit circle. The formula for the product of polynomials of the Boas-Buck type is obtained.     

Measurement of the photoneutron flux density distribution from cylindrical targets

Measurements are performed of the density of photoneutron fluxes from cylindrical targets of²H₂O (diameter 64 and height 86 mm), Be (outer diameter 70, inner diameter 40, height 100mm), and²³⁸U (diameter 44.5 mm, height 50 mm) under the action of braking radiation from electrons with energies of 4 to 8 MeV in order to determine the effect of target form and orientation relative to the detector upon the recorded photoneutron level. The fluxes were measured by an all-wave neutron detector based on an SNM-11 counter in a paraffin retarder at an angle of 90 to the axis of the braking radiation beam for various target orientations relative to the detector. Measurement results are compared to calculations. Photoneutron fluxes from heavy water and beryllium targets of the indicated dimensions were also measured for angles of 90, 135, and 167. An isotropic nature was noted in the photoneutron fluxes from both targets.Deceased.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 5–9, September, 1989.In conclusion, the authors express their gratitude to V. I. Lunev and B. M. Yakovlev for their assistance in performing the measurements.